May 1112, 2011
STOCHASTIC ACTIVITY MONTH
Workshop on
Random Graphs and the Brain
Summary
The meeting
combines researchers from random graphs and complex networks, and from
neuroscience. The aim is to obtain a better understanding of how random graphs,
or probability theory in general, can play a role in neuroscience.
This workshop fits within the framework of the SAM
Organisers
Registration
Registration is obligatory for all participants
(organizers and speakers too!).
Registration fee is 75 euros, to be paid by all
participants (excluding speakers and TU/e personnel)
Please follow the
link to the online registration. (closed)
(For the registration form you will be
redirected to the website of the Eindhoven University of Technology)
Invited speakers
Deijfen, Mia 
Stockholm University 
Dommers, Sander 
Eindhoven University of Technology 
Gómez, Vicenç 
Radboud University Nijmegen 
Memmesheimer, RaoulMartin 
Radboud University Nijmegen 
Roudi, Yasser 
Kavli Insitute, NTNU 
Straaten, Ilse van 
VU Medical Center 
Turova, Tatyana 
Lund University 
Van
Mieghem, Piet 
Delft University of Technology 
Programme
Wednesday May 11
Thursday May 12
Abstracts
Mia Deijfen
Scalefree percolation
I will describe a model for inhomogeneous longrange percolation
on Z^d with potential applications in neuroscience. Each vertex is independently
assigned a nonnegative random weight and the probability that there is an edge
between two given vertices is then determined by a certain function of their
weights and of the distance between them. The results concern the degree
distribution in the resulting graph, the percolation properties of the graph and
the graph distance between remote pairs of vertices. The model interpolates
between longrange percolation and inhomogeneous random graphs, and is shown to
inherit the interesting features of both these model classes.
PRESENTATION
Sander Dommers
Ising models on powerlaw random graphs
We study a ferromagnetic Ising model on random graphs with a powerlaw
degree distribution and compute the thermodynamic limit of the pressure when the
mean degree is finite (degree exponent $\tau > 2$), for which the random graph
has a treelike structure. For this, we adapt and simplify an analysis by Dembo
and Montanari, which assumes finite variance degrees ($\tau > 3$). We further
identify the thermodynamic limits of various physical quantities, such as the
magnetization and the internal energy.
(Joint work with C. Giardinŕ and R. van der Hofstad).
PRESENTATION
Vicenç Gómez
Selforganization using synaptic plasticity
Large networks of spiking neurons show abrupt changes in their collective
dynamics resembling phase transitions studied in statistical physics. An example
of this phenomenon is the transition from irregular, noisedriven dynamics to
regular, selfsustained behavior observed in networks of integrateandfire
neurons as the interaction strength between the neurons increases. In this work
we show how a network of spiking neurons is able to selforganize towards a
critical state for which the range of possible interspikeintervals (dynamic
range) is maximized. Selforganization occurs via synaptic dynamics that we
analytically derive. The resulting plasticity rule is defined locally so that
global homeostasis near the critical state is achieved by local regulation of
individual synapses.
PRESENTATION
RaoulMartin Memmesheimer
Irregular spiking activity in random neural networks
Mean field theory for infinite sparse networks of spiking neurons shows that
a chaotic balanced state of highly irregular activity arises under a variety of
conditions. The state is considered a model for the ground state of cortical
activity. We analytically investigate the irregular dynamics of a balanced state
in finite random networks keeping track of all individual spike times and the
identities of individual neurons. For delayed, purely inhibitory interactions,
we show that the dynamics is not chaotic but in fact stable. Moreover, we
demonstrate that after long transients the dynamics converges towards periodic
orbits and that every generic periodic orbit of these dynamical systems is
stable. These results indicate that chaotic and stable dynamics are equally
capable of generating the irregular neuronal activity. More generally, chaos
apparently is not essential for generating high irregularity of balanced
activity, and we suggest that a mechanism different from chaos and stochasticity
significantly contributes to irregular activity in cortical circuits.
PRESENTATION
Yasser Roudi
Meanfields theory for nonequilibrium network reconstruction
and applications to neural data
With the advancement of multielectrode recording, an important and
interesting question is arising: can we infer interactions between neurons from
the simultaneous observation of spike trains from many neurons? In this talk, I
first describe a toy version of this problem:
how can we infer interactions of an Ising model from observing its state
samples? I will start by a short review of how this could be done for
equilibrium systems and then study how Dynamical MeanField (naive mean field
and TAP) theory can be developed for a nonequilibrium Ising model and exploited
for inferring the network connectivity. Finally, I will describe how all this
can be used to for inferring connectivity from neural multielectrode
recordings.
PRESENTATION
Ilse Straaten
How to capture functional connectivity in the Brain
How can different, specialized brain areas communicate with each other in
order to come to a high level of functioning, such as consciousness, attention,
and various cognitive functions? The brain is complex. Proper functioning
requires both the segregation as well as the integration of information
processing. One of the central questions in neuroscience is how this integration
takes place. Neurons have intrinsic electrical firing properties and they tend
to synchronize this activity with great precision when they are connected.
Synchronization of neuronal activity is therefore a sign of functional
connectivity. Time series of brain activity can be measured with EEG, MEG, and
fMRI in various brain areas and several methods exist for determining the
strength of correlation between these regional time series. One of the nonlinear
methods, the phase lag index (PLI), will be discussed in more detail. With a
large number of measurement points on the skull (the nodes in the network), the
result is a large matrix of correlation values. When modeled as graphs, concepts
and analytical measures derived from modern network theory can be applied. As it
turns out, healthy brains of subjects in eyesclosed restingstate show a
smallworld modular structure, characterized by various properties such as
sparse connectivity, high clustering, short pathlengths between any two network
points, skewed degree distributions, presence of highly connected and central
hubs and a hierarchical architecture with modules and subnetworks. Optimal
brain function requires efficient underlying anatomical networks. The MRI
technique of diffusion tensor imaging (DTI) is capable of visualizing the
cerebral anatomical wiring. A smallworld organization was also found for these
structural networks. Although functional and anatomical networks are not
overlapping completely, analogies can be found. More recently, functional
changes in several neurological and psychiatrical disorders have been studied.
Some of these will be discussed among which Alzheimer’s disease and brain
tumors. In addition, modeling can be used to understand the rules underlying
brain network development and changes in several types of disease. All together,
the field of network science has provided a complete new view on neuronal
function and disease.
PRESENTATION
Tatyana Turova
The emergence of connectivity in neuronal networks: from
bootstrap percolation to autoassociative memory
We consider some examples of models for neural networks (accepted by the
neurophysiological
community) where the underlying graph of connections is random. We show that an
architecture with almost equal numbers of in and outconnections can emerge
naturally in a class of networks with random connections, and an exact example
of such a network is provided. It is proved that the set of parameters under
which the propagation of excitation has a constant speed is rather small within
the whole space of possible parameters.
We shall discuss which properties of random graphs are relevant for the neuro 
physiological studies. In particular, we argue that the threshold of
connectivity for an autoassociative memory in a Hopfield model with a random
connection matrix coincides with the threshold for bootstrap percolation on the
corresponding random graph.
PRESENTATION
Piet Van Mieghem
Measuring randomness and structure in complex networks
What is the relations between the properties of a complex
network and the amount of randomness and structure in that complex network? It
is conjectured that the randomness of a brain network reduces from birth with
age and that the process of learning creates structure in the brain. We will
briefly summarize the techniques to measure randomness and propose new methods
for measuring randomness and structure in networks. The method will be applied
to a set of Altzheimer patients and a set of "healthy controls".
This work is in collaboration with the group of Professor Stam (VUMc,
Amsterdam).
PRESENTATION
Practical
information
Conference Location
The workshop location is EURANDOM, Den Dolech 2, 5612 AZ
Eindhoven, Laplace Building, 1st floor, LG 1.105.
EURANDOM is located on the campus of
Eindhoven
University of Technology, in the
'Laplacegebouw' building' (LG on the map). The university is located at
10 minutes walking distance from Eindhoven railway station (take the exit
north side and walk towards the tall building on the right with the sign TU/e).
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
Contact
For more information please contact
Mrs. Patty Koorn,
Workshop officer of
EURANDOM
Sponsored by:
STAR
StochasticsTheoretical and
Applied Research
Last updated
140711,
by
PK
